Newton’s Laws of Motion

1. Newton’s Laws of Motion LG: TSW be able to analyze situations in which a particle remains at rest or moves due to influences of forces.

2. The space shuttle Endeavorlifts off for an 11-day mission in space. All of Newton’s laws of motion - the law of inertia, action-reaction, and the acceleration produced by a resultant force -are exhibited during this lift-off. Credit: NASA Marshall Space Flight Center (NASA-MSFC). NASA

3. SECOND LAW OF MOTION If there is a net force acting on an object, the object will have an acceleration and the object’s velocity will change. Newton's Second Law of Motionstatesthat for a particular force, the acceleration of an object is directly proportional to the net force and inversely proportional to the mass of the object. The direction of the force is the same as that of the acceleration. In equation form:

4. SECOND LAW OF MOTION  In the SI system, the unit for force is the newton(N): A newtonis that net force which, when applied to a 1-kg mass, gives it an acceleration of 1 m/s2.

6. Acceleration and Force With Zero Friction Forces Pushing the cart with twice the force produces twice the acceleration. Three times the force triples the acceleration.

7. Acceleration and Mass Again With Zero Friction F F a/2 a Pushing two carts with same force Fproduces one-half the acceleration. The acceleration varies inverselywith the mass.

8. THIRD LAW OF MOTION  According to Newton's third law of motion, when one body exerts a force on another body, the second body exerts on the first an equal force in opposite direction. The Third Law of Motion applies totwo different forces on two different objects: "For every action force, there must be an equal and opposite reaction force. " Action and reaction forces never balance out because they act on different objects.

9. Newton’s Third Law Third Law:For every action force, there must be an equal and opposite reaction force. Forces occur in pairs. Action Reaction Action Reaction

10. Acting and Reacting Forces Use the words by and on to study action/reaction forces below as they relate to the hand and the bar: Action Reaction The action force is exerted by the _____ on the _____. hands bar The reaction force is exerted bythe _____ on the _____. bar hands

11. MASS The property that a body has of resisting any change in its state of rest or of uniform motion is called inertia. The inertia of a body is related to the amount of matter it contains. A quantitative measure of inertia is mass. The unit of mass is the kilogram (kg).

12. WEIGHT (FG) Weight(a vector quantity) is different from mass (a scalar quantity). The weight of a body varies with its location near the Earth (or other astronomical body), whereas its mass is the same everywhere in the universe. The weight of a body is the force that causes it to be accelerated downward with theacceleration of gravity g. FG= mgUnits: Newtons (N) g = acceleration due to gravity = 9.81 m/s2

14. FORCE An object that experiences a pushor apullhas a forceexerted on it. Notice that it is the objectthat is considered. The object is called thesystem. The world around the object that exerts forces on it is called the environment. system

15. FORCE Forces can act either through the physical contact of two objects (contact forces: push or pull) or at a distance (field forces: magnetic force, gravitational force).

16. Type of Force and its Symbol Description of Force Direction of Force Applied Force An applied force is a force that is applied to an object by another object or by a person. If a person is pushing a desk across the room, then there is an applied force acting upon the desk. The applied force is the force exerted on the desk by the person. In the direction of the pull or push. FA

17. Type of Force and its Symbol Description of Force Direction of Force Normal Force The normal force is the support force exerted upon an object that is in contact with another stable object. For example, if a book is resting upon a surface, then the surface is exerting an upward force upon the book in order to support the weight of the book. The normal force is always perpendicular to the surface Perpendicular to the surface FN

18. THE NORMAL FORCE Anormal forceis a force exerted by one surface on another in a direction perpendicular to the surface of contact. Note: The gravitational force and the normal force are not an action-reaction pair.

19. Type of Force and its Symbol Description of Force Direction of Force Friction Force The friction force is the force exerted by a surface as an object moves across it or makes an effort to move across it. The friction force opposes the motion of the object. For example, if a book moves across the surface of a desk, the desk exerts a friction force in the direction opposite to the motion of the book. Opposite to the motion of the object FF

20. Type of Force and its Symbol Description of Force Direction of Force Air Resistance Force Air resistance is a special type of frictional force that acts upon objects as they travel through the air. Like all frictional forces, the force of air resistance always opposes the motion of the object. This force will frequently be ignored due to its negligible magnitude. It is most noticeable for objects that travel at high speeds (e.g., a skydiver or a downhill skier) or for objects with large surface areas. Opposite to the motion of the object FD

21. Type of Force and its Symbol Description of Force Direction of Force Tensional Force Tension is the force that is transmitted through a string, rope, or wire when it is pulled tight by forces acting at each end. The tensional force is directed along the wire and pulls equally on the objects on either end of the wire. In the direction of the pull FT

22. Type of Force and its Symbol Description of Force Direction of Force Gravitational Force (also known as Weight) The force of gravity is the force with which the earth, moon, or other massive body attracts an object towards itself. By definition, this is the weight of the object. All objects upon earth experience a force of gravity that is directed "downward" towards the center of the earth. The force of gravity on an object on earth is always equal to the weight of the object. Straight downward Fg

23. FORCES HAVE AGENTS Each force has a specific identifiable, immediate cause called agent. You should be able to name the agent of each force, for example the force of the desk or your hand on your book. The agent can be animate such as a person, or inanimate such as a desk, floor or a magnet. The agent for the force of gravity is Earth's mass. If you can't name an agent, the force doesn't exist. agent

24. A free-body-diagram (FBD) is a vector diagram that shows all the forces that act on an object whose motion is being studied.  Directions: “Book resting on a Table” - Choose a coordinate system defining the positive direction of motion. - Replace the object by a dot and locate it in the center of the coordinate system. - Draw arrows to represent the forces acting on the system.

25. 600 300 50 N Example of Free Body Diagram B By A A B Ay 300 600 Ax Bx Fg 1. Draw and label a sketch. 2. Draw and label vector force diagram. (FBD) 3. Label x and y components opposite and adjacent to angles.

26. FN FG

27. FN FG

28. FN FF FG

29. FN FGY FGX FG

30. FN FF FG

31. FT FG

32. FT1 FT2 FG

33. FT1 FT2 FG

34. FN FT FG

35. FN1 FN2 FG

36. FN FF FA FG

37. FN FA θ FF FG

38. FT FG

39. FN FF θ FA FG

40. FG

41. FD FG

42. 17.The ball has been punted by a football player. FG

43. 4.1 A 5.0-kg object is to be given an upward acceleration of 0.3 m/s2 by a rope pulling straight upward on it. What must be the tension in the rope? 5kg m = 5 kg a = 0.3 m/s2 ΣFy = FT - FG = ma FT = m(a + g) = 5(0.3 + 9.8) = 50.5 N FT a (+) FG

44. 7kg 9 kg 4.2 A cord passing over a frictionless pulley has a 7.0 kg mass hanging from one end and a 9.0-kg mass hanging from the other. (This arrangement is called Atwood's machine). a. Find the acceleration of the masses. m1 = 7 kg m2 = 9 kg FT FT a (+) a (+) FG1 FG2

45. FT FT a (+) a (+) ΣF= FT - FG1 - FT + FG2 = mTOTALa FG1 FG2 = 1.22 m/s2

46. FT FT b. Find the tension of the cord a (+) a (+) Using either side of the pulley yields the same answer! FT – FG1 = m1a FT = m1a + FG1 = m1 (a + g) = 7(1.22 + 9.8) = 77.1 N FG1 FG2

47. APPARENT WEIGHT Theactual weight of a body is the gravitational force that acts on it. The body's apparent weightis the force the body exerts on whatever it rests on. Apparent weight can be thought of as thereading on a scalea body is placed on. scale

48. 4.3 What will a spring scale read for the weight of a 75 kg man in an elevator that moves at a constant velocity: m = 75 kg FG = 75(9.8) = 735 N

49. a. With constant upward speed of 5 m/s N1L FN m = 75 kg FG = 735 N ΣFy = FN - FG = 0 FN = FG = 735 N FG b. With constant downward speed of 5 m/s FN= 735 N

50. FN ΣF = FN - FG = ma FN = ma + FG = 75 (2.45) + 735 = 919 N c. Going up with an acceleration of 0.25 g a = 2.45 m/s2 FG